In quadrilater ABCD side BC parallel side AD. Diagonal AC and diagonal BD intersect in point Q. If AQ=1/3AC, then show that DQ=1/2BQ
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Answer:
Given: in quadrilateral ABCD,
AD ║ BC and AQ=1/3 AC
To prove: DQ=1/2 BQ
Proof:
Since, AQ=1/3 AC
⇒ AQ/AC = 1/3
Let, AQ = x and AC = 3x
Where x is any number,
⇒ CQ = AC - AQ = 3x - x = 2x
Now, In quadrilateral ABCD,
AD ║ BC
By the Alternative interior angle theorem,
,
By AA similarity postulate,
Now, By the property of similar triangles,
Hence, Proved.
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